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Perturbation bounds on the extremal singular values of a matrix after appending a column
In this paper, we study the perturbation of the extreme singular values of a
matrix in the particular case where it is obtained after appending an arbitrary
column vector. Such results have many applications in bifurcation theory,
signal processing, control theory and many other fields. In the first part of
this paper, we review and compare various bounds from recent research papers on
this subject. We also present a new lower bound and a new upper bound on the
perturbation of the operator norm is provided. Simple proofs are provided,
based on the study of the characteristic polynomial rather than on variational
methods, as e.g. in \cite{Li-Li}. In a second part of the paper, we present
applications to signal processing and control theory